1. Field of the Invention
The present invention relates to a method for determining positions of targets by bistatic measurements using signals scattered by the targets. Also the velocities of the targets can be determined. The method comprises a rapid bistatic association method which is suitable for, for instance, a network of radar stations in the manner of MSR (Associative Aperture Synthesis Radar) although there may be further fields of application. AASR is described, inter alia, in U.S. Pat. No. 6,850,186, which is herewith incorporated by reference. In the following, the description will be concentrated on the new method of associating by bistatic measurements only.
2. Description of the Related Art
First the fundamental problem that is solved by the invention will be presented. Ns stations (for instance radar stations) are imagined to be set out in the space (R3). The stations are designated sj, j=1, . . . Ns and their position vectors are designated ρj, j=1, . . . Ns. In addition to the stations, there are also Nt moving targets which are to be detected. They are designated ti, i=1, . . . Nt and have corresponding time-dependent position vectors ri=ri(t), i=1, . . . Nt.
Each station is capable of measuring distances (up to a certain maximum distance) and radial speed for each target. Thus, the station sj, 1≦j≦Ns will, at a certain point of time, measuredj(k)=|rk−ρj|, k=1, 2, . . . Ndj≦Ntvj(k)=(d/dt)|rk−ρj|, k=1, 2, . . . Ndj≦Nt
For stations that are sufficiently close to each other, also bistatic measurement information is obtained, i.e. transmitting from one station and registration at another. For the pair of stations (si, sj) it means that the following is registereddij(k)=|rk−ρi|+|rk−ρj|=di(k)+dj(k), k=1, 2, . . . Ndij≦Ntvij(k)=(d/dt)|rk−ρi|+(d/dt)|rk−ρj|=vi(k)+vj(k), k=1, 2, Ndij≦Nt
It is to be noted that with these designations, dii(k)=2di(k), vii(k)=2vi(k), i=1,2, . . . , k=1,2, . . . .
For each sensor (monostatic or bistatic geometry) targets are thus registered in respect of distance and Doppler. It is a priori not possible to know which registration from one sensor is associated with a certain registration from another sensor, i.e. originating from the same target. If registrations from different sensors are paired incorrectly, false targets, ghost targets, arise. The problem of association is to discriminate, among all conceivable possibilities of combining sensor data, corresponding to conceivable target candidates, between correct combinations (targets) and false combinations (ghosts).
The maybe most straight-forward method is to consider three neighbouring stations and their monostatic registrations, which for the sake of simplicity are assumed to be N in number. These measurements can be combined in N3 ways where each combination corresponds to a target position which is determined up to reflection in the plane containing the three stations. (Certain combinations can be incompatible, corresponding to false candidates.) These ˜N3 candidates can then one by one be compared with the bistatic measurements and either be rejected or accepted. The problem of such a method is that it will be very slow if the number of targets, N, is large. For this reason, more efficient association algorithms have been developed.
Each target is to be determined in respect of position as well as velocity, i.e. they are to be positioned in a six-dimensional state space. The number of cells in the state space can be very large (˜1018), which means that traditional projection methods will be irretrievably slow.
The above Swedish Patent 0101661-7 discloses a method of attacking the problem of association by designing a sensor network so that each target is registered by many sensors (monostatic and bistatic), i.e. a high degree of redundancy is obtained in the system. Then the state space is divided into a manageable number of relatively large cells.
If the cells are just large enough, it will be possible to reject many of them, i.e. they cannot contain any targets, for the following reasons. If the cell contains a target, all (or almost all) of the possible sensors that can register targets in the current cell, will indicate such a registration. On the other hand, if the cell is empty, some sensors, and yet not too many, will still indicate registrations (from other targets) that are compatible with the cell in question. Owing to redundancy, a sufficient number of sensors will indicate the cell as empty, and it can be rejected. When the number of cells is thus reduced, the surviving cells are divided into smaller cells and the process is repeated. The process is repeated until the cells in the state space have reached the desired size. As the cells are becoming smaller, fewer and fewer ghost targets will survive, so that, when interrupting the process, practically only real targets are left. What speaks in favour of this method is that it uses (but also requires) the redundancy of the sensor network. However, it is not yet quite clear how rapid the method may eventually be.
An alternative method is disclosed in U.S. Pat. No. 6,954,404, which is herewith incorporated by reference, and implies that use is made of certain symmetries of the combination sensors—measurement data. Given two stations, the two monostatic measurements, together with the bistatic measurement, will share a symmetry, viz. that the three measuring geometries are all insensitive to rotation of the targets about the axis extending through the two stations. This means that it is possible to make an initial rapid screening of the candidates and delete a large number of false associations (ghosts). The subsequent final association will then be significantly more rapid. A drawback, however, is that the monostatic measurements will be important, which may be disadvantageous in connection with reconnaissance of stealth targets.